Gradient model of termoelasticity for laminated composite structures
Mathematics. Physics. Mechanics
Аuthors1*, 2**, 2***
1. Institute of Applied Mechanics of Russian Academy of Science, IAM RAS, 32a, Leninskii av., Moscow, В-334, GSP-1, 119991, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
Local stress fields concentrated near the interfaces of layered composite materials and excited by thermal loads are investigated on the groundwork of the gradient thermoelasticity theory. The new model of gradient thermal conductivity for layered composites is proposed to analytically describe the thermal barrier properties of not modeled interfaces by the classical heat conductivity theory. The barrier effect modeling becomes possible due to the raised order of the equations of the gradient thermoelasticity and heat conductivity models as compared with the classical ones, so that the boundary conditions of new types can be formulated. The proposed model allows one to define both deformations and normal stresses on the interfaces of composite structures subjected to thermal loads.
The new model is used to formulate the one-dimensional problem of the gradient thermoelasticity and heat conductivity for the layered structure as a boundary value problem for the system of linear ordinary differential equations with constant coefficients, therefore the analytical solution on the basis of the elementary functions becomes possible, so that allows one to perform the qualitative and quantitative analysis of the barrier effects to the stress state and strength of the composite structure.
The five-layer one-dimensional structure loaded by the temperature field is considered as a test example. The formulation of the boundary value problem is shown and the physical meaning of the boundary conditions of the new type provided by the gradient model is briefly discussed. An analytical solution is obtained. It is shown that the small scale factor results the boundary layer type of the solution with high-amplitude stress peaks concentrated at the boundary points. These effects cannot be described by the classical thermoelasticity model even in the 3D problem formulation. It may be supposed that these stress peaks can result also the known effect of cracking on the composite interfaces discussed in many modern publications.
Therefore the proposed model can become a versatile and efficient way to compute the stress state of heat-loaded composite materials, and it can be used for the composite structures design in engineering practice.
Keywords:gradient theory of elasticity, thermoelasticity, layered composites, stress-strain state, thermo-barrier properties of interfaces
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